A reduction of 20% in the price of salt enabled a purchaser to obtain 4 kg, more for Rs. 100. The reduced price of salt per kg. is = ?

Answer: Option B

Let the original price of salt per kg. is Rs. x
So, purchaser can buy $$\frac{100}{x}$$ kg.
Now, reduction price is 20%
Salt per kg. $$=x\times \frac{80}{100}=\text{Rs}\text{.}\frac{4x}{5}$$
Now purchaser can buy
$$\begin{array}{rl}& \frac{100}{\frac{4x}{5}}=\frac{125}{x}\text{kg}\\ & \therefore \frac{125}{x}-\frac{100}{x}=4\text{kg}\\ & \Rightarrow \frac{25}{x}=4\\ & \Rightarrow x=\text{Rs}\text{.}6.25\end{array}$$
Hence the reduced price of salt per kg.
$$\begin{array}{rl}& =\text{Rs}\text{.}6.25\times \frac{80}{100}\\ & =\text{Rs}\text{.}5/\text{kg.}\end{array}$$

Alternate:
$$\begin{array}{rl}& \text{Trick}=\frac{a}{x}\times \frac{\text{reduction}}{100}\\ & =\frac{100}{4}\times \frac{20}{100}\\ & =\text{Rs}\text{.}5/\text{kg.}\end{array}$$